%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP195-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:26 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 65 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 85 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 14 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 78 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) )
<=> ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) )
<=> ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) )
<=> ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) )
| ( multiply(multiply(a,multiply(b,multiply(b,multiply(b,b)))),multiply(a,a)) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(multiply(a,multiply(b,multiply(b,multiply(b,b)))),multiply(a,a)) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b)))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(b,multiply(b,b))) = multiply(a,multiply(b,multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(multiply(a,b),multiply(b,multiply(b,b))) = multiply(a,multiply(b,multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiply(multiply(multiply(a,b),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(a,multiply(b,multiply(b,multiply(b,b)))),multiply(a,a)),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(a,b),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(a,b),multiply(multiply(b,multiply(b,b)),multiply(a,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
multiply(multiply(multiply(a,b),multiply(b,multiply(b,b))),multiply(a,a)) = multiply(multiply(a,b),multiply(multiply(b,multiply(b,b)),multiply(a,a))),
inference(unit_resolution,[status(thm)],[20,16]) ).
tff(22,plain,
multiply(multiply(a,b),multiply(multiply(b,multiply(b,b)),multiply(a,a))) = multiply(multiply(multiply(a,b),multiply(b,multiply(b,b))),multiply(a,a)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
multiply(multiply(a,b),multiply(multiply(b,multiply(b,b)),multiply(a,a))) = multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b)))))),
inference(transitivity,[status(thm)],[22,19,9]) ).
tff(24,plain,
multiply(a,multiply(multiply(a,b),multiply(multiply(b,multiply(b,b)),multiply(a,a)))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,b)),multiply(multiply(b,multiply(b,b)),multiply(a,a))) = multiply(a,multiply(multiply(a,b),multiply(multiply(b,multiply(b,b)),multiply(a,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
multiply(multiply(a,multiply(a,b)),multiply(multiply(b,multiply(b,b)),multiply(a,a))) = multiply(a,multiply(multiply(a,b),multiply(multiply(b,multiply(b,b)),multiply(a,a)))),
inference(unit_resolution,[status(thm)],[25,16]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) )
| ( multiply(multiply(b,multiply(b,b)),multiply(a,a)) = multiply(a,multiply(a,multiply(b,multiply(b,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
multiply(multiply(b,multiply(b,b)),multiply(a,a)) = multiply(a,multiply(a,multiply(b,multiply(b,b)))),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
multiply(a,multiply(a,multiply(b,multiply(b,b)))) = multiply(multiply(b,multiply(b,b)),multiply(a,a)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(b,b)) = multiply(a,multiply(b,multiply(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
multiply(multiply(a,b),multiply(b,b)) = multiply(a,multiply(b,multiply(b,b))),
inference(unit_resolution,[status(thm)],[30,16]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) )
| ( multiply(multiply(a,b),multiply(b,b)) = multiply(b,multiply(b,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
multiply(multiply(a,b),multiply(b,b)) = multiply(b,multiply(b,multiply(a,b))),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
multiply(b,multiply(b,multiply(a,b))) = multiply(multiply(a,b),multiply(b,b)),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
multiply(b,multiply(b,multiply(a,b))) = multiply(a,multiply(b,multiply(b,b))),
inference(transitivity,[status(thm)],[34,31]) ).
tff(36,plain,
multiply(a,multiply(b,multiply(b,multiply(a,b)))) = multiply(a,multiply(a,multiply(b,multiply(b,b)))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(b,multiply(a,b))) = multiply(a,multiply(b,multiply(b,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
multiply(multiply(a,b),multiply(b,multiply(a,b))) = multiply(a,multiply(b,multiply(b,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[37,16]) ).
tff(39,plain,
multiply(multiply(a,b),multiply(b,multiply(a,b))) = multiply(multiply(b,multiply(b,b)),multiply(a,a)),
inference(transitivity,[status(thm)],[38,36,29]) ).
tff(40,plain,
multiply(multiply(a,multiply(a,b)),multiply(multiply(a,b),multiply(b,multiply(a,b)))) = multiply(multiply(a,multiply(a,b)),multiply(multiply(b,multiply(b,b)),multiply(a,a))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,multiply(a,b)),multiply(multiply(a,b),multiply(b,multiply(a,b)))) = multiply(a,multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
multiply(multiply(a,multiply(a,b)),multiply(multiply(a,b),multiply(b,multiply(a,b)))) = multiply(a,multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[41,16]) ).
tff(43,plain,
multiply(a,multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,b))))) = multiply(multiply(a,multiply(a,b)),multiply(multiply(a,b),multiply(b,multiply(a,b)))),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)) )
| ( multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,b))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,b))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,b)))),
inference(unit_resolution,[status(thm)],[44,7]) ).
tff(46,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(a,b)) = multiply(a,multiply(b,multiply(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
multiply(multiply(a,b),multiply(a,b)) = multiply(a,multiply(b,multiply(a,b))),
inference(unit_resolution,[status(thm)],[46,16]) ).
tff(48,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),b) = multiply(b,multiply(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
multiply(multiply(b,a),b) = multiply(b,multiply(a,b)),
inference(unit_resolution,[status(thm)],[48,16]) ).
tff(50,plain,
multiply(b,multiply(a,b)) = multiply(multiply(b,a),b),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,b))) = multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,b)))),
inference(monotonicity,[status(thm)],[50,47]) ).
tff(52,plain,
multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,multiply(a,b)),multiply(multiply(a,b),multiply(a,b))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,b)))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(unit_resolution,[status(thm)],[53,16]) ).
tff(55,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(multiply(multiply(b,a),b),multiply(a,multiply(b,multiply(a,b)))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))) = multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))),
inference(unit_resolution,[status(thm)],[56,16]) ).
tff(58,plain,
multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(b,a),multiply(b,multiply(a,multiply(b,multiply(a,b))))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b)))))) = multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,b)))),
inference(transitivity,[status(thm)],[58,55,52,45]) ).
tff(60,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(a,multiply(multiply(a,b),multiply(multiply(a,b),multiply(b,multiply(a,b))))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) = multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),
inference(transitivity,[status(thm)],[60,43,40,26,24]) ).
tff(62,plain,
( ( multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))) )
<=> ( multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(64,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP195-1 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 15:47:18 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% See solution above
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------